In a typical response surface study, an experimenter will fit a first order model in the early stages of the study and obtain the path of steepest ascent. The path leads the experimenter out of this initial region of interest and into a new region of interest. The experimenter may fit another first order model here or, if curvature is believed to be present in the underlying system, a second order model. In the final stages of the study, the experimenter fits a second order model and typically contracts the region of interest as the levels of the factors that optimize the response are nearly determined.
Due to the sequential nature of experimentation in a typical response surface study, the experimenter may find himself/herself wanting to augment some initial design with additional runs within the current region of interest. The little discussion that exists in the statistical literature suggests adding runs sequentially in a conditional D-optimal manner. Four prediction oriented criteria, I<sub>IV</sub>, I<sub>SV</sub><sub>r</sub>, I<sub>SV</sub><sub>r</sub><sup>ADJ</sup> and G, and two estimation oriented criteria, A and E, are studied here as other possible sequential design augmentation optimality criteria. Analytical properties of I<sub>IV</sub>, I<sub>SV</sub><sub>r</sub>, and A are developed within the context of the design augmentation problem. I<sub>SV</sub><sub>r</sub> is found to be somewhat ineffective in actual sequential design augmentation situations. A new more effective criterion,I<sub>SV</sub><sub>r</sub><sup>ADJ</sup> is introduced and thoroughly developed.
Software is developed which allows sequential design augmentation via these seven criteria. Unlike existing design augmentation software, all locations within the current region of interest are eligible for inclusion in the augmenting design (a continuous candidate list).
Case studies were performed. For a first order model there was negligible difference in the prediction variance properties of the designs generated via sequential augmentation by D and the A best of the other criteria, I<sub>IV</sub>, I<sub>SV</sub><sub>r</sub><sup>ADJ</sup>, and A. For a second order model, however, the designs generated via sequential augmentation by D place too few runs too late in the interior of the region of interest. Thus, designs generated via sequential augmentation by D yield inferior prediction variance properties to the designs generated via I<sub>IV</sub>, I<sub>SV</sub><sub>r</sub><sup>ADJ</sup>, and A. The D-efficiencies of the designs generated via sequential augmentation by I<sub>IV</sub>, I<sub>SV</sub><sub>r</sub><sup>ADJ</sup>, and A range from the reasonable to fully D-optimum. Therefore, the I<sub>IV</sub>, I<sub>SV</sub><sub>r</sub><sup>ADJ</sup>, optimality criteria are recommended for sequential design augmentation when quality of prediction is more important than quality in estimation of coefficients. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/39015 |
| Date | 03 August 2007 |
| Creators | Rozum, Michael A. |
| Contributors | Statistics, Myers, Raymond H., Birch, Jeffrey B., Smith, Eric P., Holtzman, Golde I., Lentner, Marvin |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | xiii, 249 leaves, BTD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 22671047, LD5655.V856_1990.R698.pdf |
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